Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem

• Published in: International journal of computer mathematics Vol. 94; no. 9; pp. 1833 - 1849
• Main Authors: Chervyakov, N.I., Molahosseini, A. S., Lyakhov, P. A., Babenko, M. G., Deryabin, M. A.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02-09-2017; Taylor & Francis Ltd
• Subjects: chinese remainder theorem; Computer arithmetic; Conversion; Converters; Cryptography; Digital signal processing; Dynamic range; Fault tolerance; Number systems; residue arithmetic; Residue number systems; residue-to-binary converter; Theorems
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2016.1247439

The residue number system (RNS) is an unconventional number system which can lead to parallel and fault-tolerant arithmetic operations. However, the complexity of residue-to-binary conversion for large number of moduli reduces the overall RNS performance, and makes it inefficient for nowadays high-performance computation systems. In this paper, we present an improved approximate Chinese remainder theorem (CRT) with the aim of performing efficient residue-to-binary conversion for general RNS moduli sets. To achieve this aim, the required number of fraction bits for accurate residue-to-binary conversion is derived. Besides, a method is proposed to substitute fractional calculations by similar computations based on integer numbers to have a hardware amenable algorithm. The proposed approach results in high-speed and low-area residue-to-binary converters for general RNS moduli sets. Therefore, with this conversion method, high dynamic range residue number systems suitable for cryptography and digital signal processing can be designed.